REIT-Based Pure Property Return Indexes

ABSTRACT

The present disclosure is directed to generating REIT-based pure property return indexes. First, REIT return data is compiled from each REIT of a plurality of REITs at a predetermined frequency. Then, the generated REIT return data is de-levered and processed according to exposures to each of a plurality of target characteristics to obtain coefficients reflecting each REIT&#39;s weight in an index. Finally, an index is generated according to the REITs, the obtained coefficients, and the weights.

RELATED APPLICATIONS

This application claims priority to U.S. Provisional Application No.61/141,029, ““Pureplay” REIT-based Property Price Indexes,” filed Dec.29, 2008, the entire contents of which are incorporated herein byreference.

BACKGROUND

1. Technical Field

The present application is directed generally to REIT-based propertyreturn indexes and in particular, creating indexes of property marketreturns according to target characteristics of properties held by theREITS.

2. Description of Related Art

Growing quantities of commercial property equity assets are being heldby publicly traded securitized real estate companies, known as RealEstate Investment Trusts (REITS). Public stock exchanges are generallyregarded to be more efficient and liquid than traditional privateproperty markets, in which real estate assets trade directly inprivately negotiated transactions. However, REITs' diversificationacross geographic regions and types of property usage, as well as REITs'leverage, inhibits analysts' abilities to use REITs' liquidity formaking targeted investments according to desired characteristics ofproperty holdings.

SUMMARY

In one aspect, the present disclosure is directed to a method ofgenerating a REIT-based property return index. The method includescompiling REIT return data from each REIT of a plurality of REITs at apredetermined frequency. The method also includes de-levering thegenerated REIT return data. The method also includes processing thede-levered REIT return data according to exposures to each of aplurality of target characteristics to obtain coefficients reflectingeach REIT's weight in an index. The method also includes generating theindex according to the REITs, the obtained Coefficients, and theweights.

The target characteristics can be property market segments. The compiledREIT return data can reflect total returns or capital returns. In thelatter embodiment, the generated index is a price index. The processingcan be regression, direct calculation, and/or mathematical constrainedoptimization. The predetermined frequency can be one of monthly, daily,and real-time. Property holdings lacking the target characteristics foreach REIT used to compile REIT return data can comprise less than apredetermined percentage of the REIT's total property holdings. Thepredetermined percentage can be one of 30%, 40%, and 50%. The WeightedAverage Cost of Capital (WACC) accounting identity can be used tode-lever the generated REIT return data. The processing can account formulticollinearity among the target characteristics.

BRIEF DESCRIPTION OF THE DRAWINGS

The foregoing and other objects, aspects, features, and advantages ofthe present disclosure will become more apparent by referring to thefollowing description taken in conjunction with the accompanyingdrawings, in which:

FIG. 1 is an exemplary block diagram of a computing system forgenerating the REIT-based pure property return indexes;

FIG. 2A-2E are exemplary graphical depictions of REIT-based pureproperty price return indexes according to usage type sectors;

FIG. 3 is a table demonstrating exemplary Variance Inflation Factors(VIFs) across target property segments; and

FIG. 4A-4D are exemplary graphical depictions of REIT-based pureproperty price indexes that account for VIFs.

DETAILED DESCRIPTION

For purposes of reading the description of the various embodimentsbelow, the following descriptions of the sections of the specificationand their respective contents may be helpful:

-   -   Section A presents an overview of the REIT-Based pure property        return indexes generated according to the present disclosure;    -   Section B describes exemplary methods for generating REIT-Based        pure property return indexes;    -   Section C describes a computing system for generating the        REIT-Based pure property return indexes described herein; and    -   Section D describes exemplary demonstrations of generating        REIT-Based pure property price return indexes.

A. Overview of the REIT-Based Pure Property Return Indexes

In general overview, the present disclosure relates to systems andmethods for generating REIT-based property return indexes, such as totalreturn indexes and price indexes. Although REITs own diverse real estateassets across geographical regions and types of property, their holdingsof properties nevertheless permit careful manipulation to yieldinformation about underlying property valuations. In particular, REITsmay be manipulated to generate de-levered indexes that reflect propertyreturns for groupings of properties according to target characteristics.For example, properties may be grouped according to their segments ofthe property market. A segment may refer to a combination of propertyusage type sector(s) (e.g., apartment, industrial, office, retail,hotel), geographical region(s), economic region(s), and/or metropolitanregion(s) that defines a segment of the overall aggregate commercialproperty market. In another example, properties may be grouped accordingto characteristics such as size, gradation of urbanity (e.g., urban,suburban, or rural), extent of subjection to supply constraints, or anyother similar characteristic. As a result, the present disclosure maygenerate indexes that reflect property returns for the Northeasternhotel property market, the West Coast retail property market, theMidwestern industrial property market, small properties, largeproperties, suburban properties, urban properties, or any other suchcategory as would be appreciated by one of ordinary skill in the art.For the purposes of this disclosure, such indexes may also be referredto herein as “targeted portfolios.”

The indexes generated according to the present disclosure exhibit anumber of unique and noteworthy characteristics. First, such indexesappear to lead transactions-based direct property market indexes duringmarket turns. Such information can provide investors with opportunitiesto make pure, targeted investments in the commercial real estate marketwhile retaining the liquidity benefits of the public market via REITs.Additionally, this information may open opportunities to constructhedges in the real estate market and support derivatives trading.

Second, the indexes exhibit volatilities comparable or less thanexisting private market transaction-based indices, such as theMoody's/REAL CPPI, reflecting their accuracy as models. Third, theindexes can be generated at the high frequencies (e.g., daily orreal-time, the latter referring to data as it becomes available viaticker tape or the like) without significant increases in noise and atvarious levels of granularity for the target characteristics, therebyproviding more detailed information about property prices. Lastly, suchindexes can be directly constructed and traded via long and shortpositions taken in the publicly-traded REITs that compose the indexes.This facilitates pricing of derivatives and also enables construction ofexchange-traded funds (ETFs) that track or implement the indexes.Overall, the indexes of the present disclosure can provide accuratehigh-frequency information about property market prices and/or totalreturns that can be leveraged for a wide variety of financialinitiatives.

B. Methods of Generating the REIT-Based Pure Property Return Indexes

To determine the returns for grouping of properties by targetcharacteristics based on REITs, the return for each REIT at apredetermined interval of time may be modeled to account for each targetcharacteristic. Although the models described in the present disclosureare directed to property market segments, the structure and applicationof the model may be reformulated according to any desiredcharacteristics of the property holdings, as would be appreciated by oneof ordinary skill in the art.

Further, the models may be adjusted to produce indexes reflecting pricereturns or total returns to the groupings of properties by targetedcharacteristics. When the compiled REIT return data reflects capitalreturns, the created index tracks price returns. When the compiled REITreturn data reflects total returns, including income, the created indextracks total returns.

The particular model for the return for each REIT when modelingaccording to five usage-type property market segments may follow theformula:

r _(i,t) =b _(A,t) x _(A,i,t) +b _(O,t) x _(O,i,t) +b _(I,t) x _(I,i,t)+b _(R,t) x _(R,i,t) +b _(H,t) x _(H,i,t) +e _(i,t)

where:

b_(S,t) is the return to property market segment S at time t,

where:

x_(A,i,t)=dollar percentage of assets held by REIT i in apartmentsegment at time t

x_(O,i,t)=dollar percentage of assets held by REIT i in office segmentat time t

x_(I,i,t)=dollar percentage of assets held by REIT i in industrialsegment at time t

x_(R,i,t)=dollar percentage of assets held by REIT i in retail segmentat time t

x_(H,i,t)=dollar percentage of assets held by REIT i in hotel segment attime t

where:

x _(Ai,t) +x _(O,i,t) +x _(I,i,t) +x _(R,i,t) +x _(H,i,t)=1

and where:

e_(i,t) is an error term reflecting the idiosyncratic return of REIT iat time t

Although the model accounts for five property market segments, otherembodiments of the model may use any number of segments or any number ofgroupings of properties by target characteristics.

When the dollar value of assets in a REIT's portfolio cannot beobtained, proxies such as rental income, total square footage, or anycomparable metric may be used instead. Further, when REITs includemiscellaneous property exposures to non-targeted segments (e.g., land,garages, international assets), such exposures can be aggregated into asingle “other” segment and the dollar percentages held by targetedproperty market segments can be adjusted to sum to one (1). In thismanner, the “other” segment can be ignored and the remaining exposurescan be resealed to sum to one (1). For example, if a REIT holds 25% ofits holdings in office properties, 60% in industrial properties, and 15%in parking facilities, the office exposure can be converted to 25/85%office, the industrial exposure can be converted to 60/85% industrial,and the parking exposure can be ignored. Using this model, the returnsto real estate assets in the “other” segment can be transferred to theidiosyncratic return term, i.e. the error term. In some embodiments, aREIT is included in the index if the “other” segment does not exceed apredetermined percentage of the REIT's total holdings (e.g., 25%, 30%,40%). Otherwise, the REIT may be filtered out. As a result, the presentdisclosure can leverage information about property market segmentsincorporated into an REIT, even if the REIT contains significantholdings outside the targeted segments.

To continue development of the model, the model can be expressed inmatrix form as:

r _(levered) =Xb _(levered) +u

where r_(levered) is a vector of length N, with each elementrepresenting the monthly return to each of the i=1 . . . N REITs. X isan N×K matrix containing the dollar percentages of assets held by eachREIT in each of the k=1 . . . K segments. u is the idiosyncratic returnsof the REITs.

As previously described, REITs exhibit idiosyncratic returns attributedto assets in non-targeted property market segments, REIT-levelmanagement, and/or idiosyncratic returns within each REIT's individualproperty holdings. To obtain the most accurate pure property returnindex, any approach to generating such indexes would seek to minimizeidiosyncratic REIT return variance.

The variance of the idiosyncratic return of a REIT can be modeled asbeing inversely proportional to the total dollar value of its propertyholdings. Further, the idiosyncratic returns may be assumed to beuncorrelated, normally distributed, and have mean zero. Theidiosyncratic variance Ω of returns may be constructed according to anymethod of estimation. For example, Ω can be defined as an N×N diagonalmatrix containing the idiosyncratic REIT return variances, with eachdiagonal element defined as:

$u_{i,i}^{2} = \frac{1}{{total}_{i}}$

where total_(i) is the total dollar value of properties held by REIT i.In some embodiments, each diagonal element can be defined as:

$u_{i,i}^{2} = \frac{1}{\sqrt{{total}_{i}}}$

In this manner, property market segment returns can be estimated viageneralized least squares according to the following equation:

b _(levered)=(X ^(T)Ω⁻¹ X)⁻¹ X ^(T)Ω⁻¹ r

An intermediate step in the above process includes the determination ofthe weights for REITs in a targeted portfolio, as the following matrixlabeled H:

H _(levered)=(X ^(T)Ω⁻¹ X)⁻¹ X ^(T)Ω⁻¹

in which H_(levered) is a K×N matrix where each row k represents aportfolio of weights of REITs which has unit exposure, i.e. 100%exposure, to segment k and zero exposure to every segment other thansegment k. The property market segment weights sum to one (1) for thetarget segment and to zero (0) for the non-target segments, and mayrepresent long and short positions for the REITs. If such a portfoliowere invested, the portfolio would yield a pure return to the targetedproperty market segment while minimizing idiosyncratic REIT returnvariance.

Further, instead of regression via generalized least squares (GLS), theH matrix can be determined via direct mathematical calculation and/ormathematical constraint optimization. The weights can be determinedusing, for example, the “Solver”® feature of Microsoft Excel,manufactured by Microsoft Corporation of Redmond, Wash. One of ordinaryskill can enter the formula for the variance of the targeted portfolioin an Excel cell and instruct the “Solver”® to minimize the value in thecell subject to the following requirements: i) the weights on thetargeted segment must sum to one (1), and ii) the weights on all theother segments must sum to zero (0).

This presented method can be further refined to reduce the volatility ofthe generated index and produce more accurate data regarding propertyreturns. In particular, REITs are typically levered, holding anywherefrom 0% debt to over 50% debt. Although the estimated levered propertymarket segment returns incorporate information about underlying propertyprice movements, the leverage increases the volatility of the returns.De-levering the returns decreases the volatility of the index andproduces return data about underlying held properties.

One of the ways to de-lever the returns is to use the Weighted AverageCost of Capital (WACC) accounting identity to obtain returns on theunderlying assets (roa):

roa _(i,t)=(% equity_(i,t))·r _(i,t)+(% debt_(i,t))·debtrate_(t)

The equity percentage, also known as the equity ratio, is the totalstockholder equity divided by the sum of total stockholder equity andtotal liability as of the year-end date on 10 k forms. Such ratio datacan be updated at any desired frequency (e.g., annually or quarterly)for each year in the study. Further, the equity and debt percentages foreach REIT can be generated using financial information about the REITsfrom NAREIT and annual 10 k forms, by way of example. In someembodiments, when minority interests represent significant portions ofREIT balance sheets, the equity and debt percentages can be adjusted toaccount for such holdings. However, when these holdings areinsignificant, adjustments need not be made. The returns in the aboveformula can refer to capital returns (reflecting price changes) or totalreturns (including income).

The same debt rate may be used for all REITs. Further, the debt rate maybe calculated according to any number of methods. For example,market-wide average yields on unsecured REIT debt may be used as a proxyfor the cost of debt, and the same rate may be applied to every REIT forthe year. In some embodiments, the weighted average cost of debtreported in some REITs' annual 10 k filings may be used as the debtrate, instead. Another method of calculating the debt rate may followthe formula:

debtrate_(i,t)=(IE_(i,t)+PD_(i,t))/(0.5(TD_(i,t)+TD_(i,t−1))+0.5(PS_(i,t)+PS_(i,t−1)))

where:

IE_(i,t)=the interest expense for firm i in period t

PD_(i,t)=the preferred dividends paid by firm i in period t

TD_(i,t)=firm i's total debt balance (book value) in period t

PS_(i,t)=firm i's preferred stock at the end of year t

Although these embodiments contemplate using the same debt rate for allREITs, de-leveraging may also be accomplished by using REIT-specificvalues.

Once the calculated REIT returns are de-levered, the mathematical modelfor returns on property market segments can be written as:

roa=Xb _(delevered) +u

and the property market segment returns and weights for REITs in atargeted portfolio can be solved according to revised formulas of:

b _(delevered)=(X ^(T)Ω⁻¹ X)⁻¹ X ^(T)Ω⁻¹ roa

H _(delevered)=(X ^(T)Ω⁻¹ X)⁻¹ X ^(T)Ω⁻¹

Under these revised formulas, the estimated coefficients of b directlyreflect the returns to the underlying property segments. Thus,regression of the REIT returns against the REIT's proportional exposuresto each of the property segments produces the estimated coefficients andmay be performed, for example, via a GLS approach, which minimizes thesum of the squared errors of the regression. These regressions can becalculated for intervals of varying and/or predetermined length over anyperiod of time, thereby generating coefficients according to suchintervals. For example, REIT returns can be regressed against segmentexposures on a monthly basis to generate coefficients for each month.Likewise, the returns can be regressed on a daily basis to generatedaily coefficients. In other examples, the returns can be regressed on apooled basis. In further examples, the desired solution can be obtainedby direct mathematical calculation and/or mathematically constrainedoptimization as described in more detail, above.

The targeted portfolios contained in H_(de-levered) do not include thedebt positions needed to offset the leverage held by the REITs, becausethat leverage has already been removed. Further, the optimal relativeweights of the REITs in the targeted portfolio may be independent ofleverage and the techniques used to de-leverage the REIT returns. As aresult, scaling the coefficients calculated via regression would producethe same portfolio with varying amounts of leverage. Further, togenerate the portfolio of assets that would theoretically need to bepurchased to obtain targeted property segment-specific returns,completely adjusting for leverage, the segment portfolios would needadjustment. These adjustments can be accomplished by returning to theWACC identity for each REIT:

hadjusted_(k,i)=(% equity_(i))·h _(k,i)

debtoffset_(k,i)=(% debt_(i))·h _(k,i)

where h_(k,j) is the share (long or short) of the portfolio for targetsegment k to be invested in REIT j.

Another approach to modeling the returns for property market segmentsbased on REITs is the pureplay approach, as described by:

{tilde over (r)} _(i) =x _(A,i)({tilde over (r)} _(A) +{tilde over (e)}_(A,i))+x _(O,i)({tilde over (r)} _(O) +{tilde over (e)} _(O,i))+x_(I,i)({tilde over (r)} _(I) +{tilde over (e)} _(I,i))+ . . . +x_(K,i)({tilde over (r)} _(K) +{tilde over (e)} _(K,i))

where:

r_(i)=observed return to REIT i

{tilde over (r)}_(k)=pureplay return to segment k

x_(k,i)=fraction of REIT i invested in segment k

{tilde over (e)}_(k,i)=idiosyncratic return to REIT i's property insegment k

and where:

${\sum\limits_{K}\; x_{k,i}} = 1$

where K denotes the last of some number of segments.

The idiosyncratic components in the pureplay model are assumed to berandom, uncorrelated with each other, and have mean zero. As a pureplaymodel is defined as an index with unit exposure to the desired segmentand zero exposure to all other segments:

${\overset{\sim}{r}}_{p} = {{{\overset{\sim}{r}}_{A}{\sum\limits_{i = 1}^{N}\; {w_{i}x_{A,i}}}} + {{\overset{\sim}{r}}_{O}{\sum\limits_{i = 1}^{N}\; {w_{i}x_{O,i}}}} + \ldots + {{\overset{\sim}{r}}_{K}{\sum\limits_{i = 1}^{N}\; {w_{i}x_{K,i}}}} + {\sum\limits_{i = 1}^{N}\; \left( {{w_{i}x_{A,i}e_{A,i}} + \ldots + {w_{i}x_{K,i}e_{K,i}}} \right)}}$

where each w_(i) equals the percentage of the index's holdings in REIT iand where the constraints for a pureplay index for a single segment kcan be written mathematically as:

${\sum\limits_{i = 1}^{N}\; {\sum\limits_{j \neq k}^{\;}\; {w_{i}x_{i,j}}}} = 0$${\sum\limits_{i = 1}^{N}\; {w_{i}x_{i,k}}} = 1$

Substituting the above constraints into the formula for the pureplayindex results in a simplified equation for the return to the pureplayindex for segment k:

${\overset{\sim}{r}}_{p} = {{\overset{\sim}{r}}_{K}{\sum\limits_{i = 1}^{N}\; \left( {{w_{i}x_{A,i}e_{A,i}} + \ldots + {w_{i}x_{K,i}e_{K,i}}} \right)}}$

whose variance can be described according to:

${{VAR}\left( {\overset{\sim}{r}}_{p} \right)} = {{{VAR}\left( {\overset{\sim}{r}}_{k} \right)} + {\sum\limits_{i = 1}^{N}\; \left( {{w_{i}^{2}x_{A,i}^{2}{{Var}\left( e_{A,i} \right)}} + \ldots + {w_{i}^{2}x_{K,i}^{2}{{Var}\left( e_{K,i} \right)}}} \right)}}$

The idiosyncratic segment variance is assumed to be inverselyproportional to a REIT's dollar holdings in that segment:

${{Var}\left( e_{K,i} \right)} = \frac{1}{x_{k,i} \cdot {total}_{i}}$

Substituting this expression for segment variance into the formula forindex variance results in:

${{VAR}\left( {\overset{\sim}{r}}_{p} \right)} = {{{VAR}\left( {\overset{\sim}{r}}_{k} \right)} + {\sum\limits_{i = 1}^{N}\; \begin{pmatrix}{{w_{i}^{2}x_{A,i}^{2}\frac{1}{x_{A,i} \cdot {total}_{i}}} + \ldots +} \\{w_{i}^{2}x_{k,i}^{2}\frac{1}{x_{k,i} \cdot {total}_{i}}}\end{pmatrix}}}$

Which can be simplified to:

${{VAR}\left( {\overset{\sim}{r}}_{p} \right)} = {{{VAR}\left( {\overset{\sim}{r}}_{k} \right)} + {\sum\limits_{i = 1}^{N}\; \left( {w_{i}^{2} \cdot \frac{1}{{total}_{i}}} \right)}}$

Differentiating this equation with respect to w, for the purposes ofminimization reveals that the solution is a function of the second term.

Because of the assumptions regarding idiosyncratic returns, the varianceof the idiosyncratic returns in the pureplay model reduces to the samevariance assumption used in the previous regression models. As theprevious regression models minimized, the sum of the squared errors ofthe regression, the models minimized the variance of the error terms(i.e., the idiosyncratic returns). These variances are assumed valuescontained in Ω, as previously defined. Therefore, the regressionsolution yielding H_(de-levered) is identical to the solution tominimizing the variance of the pureplay model with respect to the w_(i).For this reason, mathematical constrained optimization yields comparabletargeted portfolio weights as regression.

Further, the presently disclosed models can be modified to achievevarying levels of granularity for property market segments. In theregression model thus described, the model targets property marketsegments such as the apartment segment, the office segment, theindustrial segment, the retail segment, and the hotel segment. In someembodiments, the model can target property market segments bygeographical region instead (e.g., Northeast, Midwest, West Coast,South), which may be defined according to the National Council of RealEstate Investment Fiduciaries's (NCREIF) convention, by way of example.

Alternatively, the model can target segments according to both usagetype of properties and geographical region. In these embodiments, themodel can account for apartment segments specific to each region, officesegments specific to each region, and so on. In further embodiments, themodel can account for any grouping of properties by targetcharacteristics, such as small properties or large properties,granularity of urbanity (urban, suburban, rural), environmental ratings(e.g., “green properties”), or the like. The model can account for anyusage type, geographical region, target characteristic, or combinationthereof as would be appreciated by one of ordinary skill in the art. Inany of these embodiments, calculated REIT returns would be regressedagainst exposures to each target segment or subject to mathematicalconstrained optimization to obtain the corresponding coefficients.

For example, to begin constructing a model that targeted geographicaland usage type segments of the property market, the following variablescould be defined:

x_(Wi,t)=dollar percentage of assets held by REIT i in the West regionat time t

x_(MW,i,t)=dollar percentage of assets held by REIT i in the Midwestregion at time t

x_(E,i,t)=dollar percentage of assets held by REIT i in the East regionat time t

x_(S,i,t)=dollar percentage of assets held by REIT i in the South regionat time t

where:

x _(Wi,t) +x _(MWi,t) +x _(E,i,t) +x _(S,i,t)=1

To achieve finer granularity on the basis of usage type, each variablein the above preliminary model can be expanded to multiple variablescovering each usage type. For example, the variable for the apartmentsegment represented by:

x_(A,i,t)=dollar percentage of assets held by REIT i in apartmentsegment at time t can be replaced with:

x_(W,A,i,t)=dollar percentage of assets held by REIT i in the west inapartment segment at time t

x_(S,A,i,t)=dollar percentage of assets held in the south in apartmentsegment at tune t

x_(E,A,i,t)=dollar percentage of assets held in the east in apartmentsegment at time t

x_(MW,A,i,t)=dollar percentage of assets held in the Midwest inapartment segment at time t

However, as the number of target property market segments grows, themulticollinearity among at least some of the segments can causeexcessive standard errors in the corresponding estimated segmentreturns. Variance inflation factors (VIFs) can quantify the severity ofthis multicollinearity and be used to mitigate the severity of themulticollinearity's effects. After property market segments with highVIFs are identified, these segments can be aggregated into less granularsegments, thereby reducing the total number of segments against whichthe REIT returns will be regressed.

The VIF is derived from the equation for the variance of the regressioncoefficients:

${{Var}\left( b_{k} \right)} = \frac{\sigma^{2}}{\left( {1 - R_{k}^{2}} \right){\sum\limits_{i = 1}^{N}\; \left( {x_{i,k} - {\overset{\_}{x}}_{k}} \right)^{2}}}$

where R_(k) ² is the R-squared from the regression of explanatoryvariable k on all explanatory variables excluding variable k. As R_(k) ²gets larger, the variance of the estimated regression coefficientbecomes larger. In the case of perfect collinearity, R_(k) ²=1 and thevariance of the estimated regression coefficient is infinite. VIF isdefined as:

${VIF}_{k} = \frac{1}{\left( {1 - R_{k}^{2}} \right)}$

In further embodiments, VIF can be determined as described in“Econometric Analysis,” 5^(th) edition, by Greene.

VIF captures the relationship between the collinearity of a variable andthe resulting increase in variance of the estimated coefficient for thevariable. The square root of the VIF measures how many times higher thestandard error of the regression coefficient is as a result ofcollinearity. A factor equal to one implies that there is nocollinearity for explanatory variable k; the standard errors are notinflated (variable k is orthogonal). A factor equal to two implies thatthe standard errors for coefficient k are twice as high as they would beif variable k was orthogonal. Thus, variables with high VIFs may beidentified and combined. Regressing the REIT returns, performing directcalculation, or mathematical constraint optimzation in light of themodified target segments results in more accurate indexes about theproperty market segments.

C. Computing System

Referring now to FIG. 1, an exemplary block diagram of a computingsystem 100 for generating characteristic-specific, de-levered indexes ofproperty market returns is shown and described. In general overview, thecomputing system 100 includes a computing device 105 with a REIT returnmodule 110, a de-leveraging module 115, and a processing module 120. Thecomputing system 100 also includes a database 125 that stores data usedto generate the indexes. In some embodiments, the database 125 caninhabit the same computing device 105 as the modules 110, 115, and 120,although in other embodiments, the database 125 can be incorporated inan external storage device.

The REIT return module 110, de-leveraging module 115, and processingmodule 120 may perform any of the computations described in reference toSection B of the present disclosure. The modules may run in software,hardware, or any combination thereof. In some embodiments, the modulesmay include any program, application, process, task, thread, or set ofexecutable instructions capable of performing any of the tasks describedherein.

The database 125 can store any REIT or other real estate-related datapertinent to generating indexes of the present disclosure. Some examplesof this data can include REIT return data, bond data, property holdingdata, or any combination thereof.

D. Exemplary Demonstrations of Generating REIT-Based Pure Property PriceReturn Indexes

Demonstrative examples of generating REIT-based pure property pricereturn indexes are herein described. In the first example, the REITsforming the basis for the index are the publically traded equity REITSlisted in the NAREIT/FTSE indices during the period 2001-2007. REITreturn data was first computed on a monthly basis for the 84 months from2001-2007 according to the following formula:

$r_{i,t} = \frac{{{REIT}\mspace{14mu} {price}_{i,t}} - {{REIT}\mspace{14mu} {price}_{i,{t - 1}}}}{{REIT}\mspace{14mu} {price}_{i,{t - 1}}}$

Such return data may be computed based on property holding informationsupplied by NAREIT, data from public SEC 10 k filings, and/or anycomparable source of information. In this example, the return data isbased on price-only returns that exclude dividends, thereby accountingfor price movements alone. Further, the REIT prices can be adjusted forsplits.

Then, the REIT return data was de-levered according to

roa _(i,t)=(% equity_(i,t))·r _(i,t)+(% debt_(i,t))·debtrate_(t)

in which financial information from NAREIT and annual 10 k filings wereused to calculate the debt and equity percentages for each REIT. Theequity and debt percentages were updated annually for each yearanalyzed. Further, because minority interests were relativelyinsignificant on the balance sheets of most REITs, the equity and debtpercentages were not adjusted for such interests.

In this example, the market-wide average yields on unsecured REIT debtwas used as a proxy for the cost of debt, with the same rate applied toevery REIT for the year. As a result, by way of example, a 5.66% debtpercentage was used for all REITs in 2007. As Boston Properties reporteda weighted average cost of debt of 5.60% and Mack-Cali Realty reported avalue of 6.08% in 2007, the estimate was reasonable. In other examples,the weighted average cost of debt reported in REIT annual 10 k filingsmay have been used instead.

GLS regressions were run for each of the eighty four months spanning2001-2007 against the apartment, office, industrial, retail, and hotelsegments. The resulting segment returns were accumulated to produce thesegment-specific indexes, which are plotted against the equivalentMoody's/REAL CPPI indexes (e.g., transactions price based indexes ofU.S. commercial property price movements in the direct private propertymarket) in FIGS. 2A-2E. The correspondence between the REIT-based andMoody's/REAL price indexes suggests that the REIT-based indices areindeed accurately reporting segment-specific returns to the underlyingproperty market. Further, the annualized volatilities of REIT-basedde-levered indexes are similar or lower than the volatilities of theMoody's/REAL indexes over the same period, as demonstrated by thefollowing table:

Apt Office Indust Retail Hotel REIT-based 4.80% 5.84% 6.46% 5.18% 10.15%Monthly Delevered Annualized Volatility Moody's/REAL 8.06% 6.27% 7.05%5.11% N/A Quarterly Annualized Volatility

As the figures demonstrate, the REIT-based de-levered data often leadsthe private market price movements. For example, the REIT-based Officeindex begins to decline in January 2007, whereas the Moody's/REALsuggests that prices in the private market did not begin to declineuntil after the following June.

For further refinement, each of the five property type segments wassubdivided into four regional market segments, yielding a total oftwenty variables. Then, for each month over the period 2001-2007, eachof the twenty segments was regressed against all the remaining segmentsto calculate VIFs. The monthly average VIF for each segment is depictedin FIG. 3, with high VIFs in bold type. Because the hotel marketsegments across the four geographical regions demonstrate high VIFs,these segments can be combined into a single segment. Further, high VIFsbetween the Industrial South and Industrial West indicate that these twosegments shall be combined, too. As a result, the 20-segment modelcollapses into a 16-segment model.

Then, the de-levered REIT return data is re-regressed according to the16-segment model. FIGS. 4A-4D depict the results for the apartment,office, industrial, and retail sectors for each geographical region,again plotted against the corresponding Moody's/REAL CPPI index.

While the invention has been particularly shown and described withreference to specific embodiments, it should be understood by thoseskilled in the art that various changes in form and detail may be madetherein without departing from the spirit and scope of the invention asdefined by the appended claims.

1. A method of generating a REIT-based property return index, the methodcomprising: compiling REIT return data from each REIT of a plurality ofREITs at a predetermined frequency; de-levering the generated REITreturn data; processing the de-levered REIT return data according toexposures to each of a plurality of target characteristics to obtaincoefficients reflecting each REIT's weight in an index; and generatingthe index according to the REITs, the obtained coefficients, and theweights.
 2. The method of claim 1, wherein the target characteristicsare property market segments.
 3. The method of claim 1, wherein thecompiled REIT return data reflects total returns.
 4. The method of claim1, wherein the compiled REIT return data reflects capital returns andthe generated index is a price index.
 5. The method of claim 1, whereinthe processing is regression.
 6. The method of claim 1, wherein theprocessing is direct calculation.
 7. The method of claim 1, wherein theprocessing is mathematical constrained optimization.
 8. The method ofclaim 1, wherein the predetermined frequency is one of monthly, daily,and real-time.
 9. The method of claim 1, wherein property holdingslacking the target characteristics for each REIT comprise less than apredetermined percentage of the REIT's total property holdings.
 10. Themethod of claim 9, wherein the predetermined percentage is one of 30%,40%, and 50%.
 11. The method of claim 1, wherein the Weighted AverageCost of Capital (WACC) accounting identity is used to de-lever thegenerated REIT return data.
 12. The method of claim 1, wherein theprocessing accounts for multicollinearity among the targetcharacteristics.